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Properties

Label 124950.ce
Number of curves $6$
Conductor $124950$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ce1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 124950.ce have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1\)
\(17\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(13\) \( 1 - 6 T + 13 T^{2}\) 1.13.ag
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 124950.ce do not have complex multiplication.

Modular form 124950.2.a.ce

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 4 q^{11} - q^{12} + 6 q^{13} + q^{16} + q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.

Elliptic curves in class 124950.ce

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.ce1 124950bc6 \([1, 1, 0, -2134660525, 37960386875125]\) \(585196747116290735872321/836876053125000\) \(1538400480845361328125000\) \([2]\) \(84934656\) \(3.9123\)  
124950.ce2 124950bc4 \([1, 1, 0, -309459525, -2095132789875]\) \(1782900110862842086081/328139630024640\) \(603207802074513615000000\) \([2]\) \(42467328\) \(3.5658\)  
124950.ce3 124950bc3 \([1, 1, 0, -134627525, 581770138125]\) \(146796951366228945601/5397929064360000\) \(9922827445201400625000000\) \([2, 2]\) \(42467328\) \(3.5658\)  
124950.ce4 124950bc2 \([1, 1, 0, -21339525, -25566829875]\) \(584614687782041281/184812061593600\) \(339733659912897600000000\) \([2, 2]\) \(21233664\) \(3.2192\)  
124950.ce5 124950bc1 \([1, 1, 0, 3748475, -2711661875]\) \(3168685387909439/3563732336640\) \(-6551086651146240000000\) \([2]\) \(10616832\) \(2.8726\) \(\Gamma_0(N)\)-optimal
124950.ce6 124950bc5 \([1, 1, 0, 52797475, 2074985113125]\) \(8854313460877886399/1016927675429790600\) \(-1869383188853741160928125000\) \([2]\) \(84934656\) \(3.9123\)